DOVER — The Dover High School girls basketball team on Wednesday night showed the poise and patience it needs to be competitive with the best teams in Division I.

Unfortunately for the Green Wave, that was only in the first half.

A 15-point lead wasn’t enough for Dover in their 2013 debut against Alvirne, as the composure that defined the first half for the Green Wave in the first half eluded them in the second en route to a 61-57 loss. The visiting Broncos used an effective press and scored 16 unanswered points in the third quarter to rally and held on for the win in the fourth.

“We weren’t being smart with the ball,” said Dover’s Katie Boyatsis. “We need more patience. After halftime, even if we have the lead, we have to come out strong. The whole game, we have to stay composed and not get too confident or too down.”

Alvirne’s Sandi Purcell scored 21 points, including 15 during the Broncos third-quarter rally. Purcell hit a pair of 3-pointers and a pair of transition buckets during Alvirne’s 16-0 run that turned a 39-24 deficit into a 40-39 lead.

“They shot the ball very well in the second half,” Dover coach Dan Casey said about Alvirne. “Their pressure was similar to the first half, but in the first half we weren’t throwing it into their outstretched arms. With the loss, Dover fell to 3-3 in D-I while the Broncos improved to 4-1.

The Broncos led 48-44 after three quarters and 59-52 after Purcell drained her fifth 3-pointer of the night with 4:30 to go. Dover held Alvirne scoreless from the field for the rest of the game but could not catch up. Boyatsis missed a pair of free throws with 1:12 to go that would have cut the deficit to two points, and Alvirne put the game on ice with free throws of their own.

“We knew Dover was going to be scrappy,” Alvirne coach Steve Tracy said. “They’re young like we are, and I knew it was going to be a close game and a tough win, if at all. It was a good game.”

“On defense, they kept pressuring us,” said Dover’s Abby Tilton. “We couldn’t work our offense because of the pressure. They kept running it and we had no time to get back.”

After a nip-and-tuck first quarter that featured four lead changes and four ties, Dover asserted itself in the second. The Green Wave led 16-14 at the end of the first and scored the first eight points of the second, including an open jumper by Molly St. Germain and a layup by Wotton following a nice dish underneath from Boyatsis. Wotton also scored on a fallaway jumper as Dover led 36-24 at the break.

“We were moving the ball the way we wanted to move the ball,” Casey said about the first half. “We made the extra pass, we were looking for the openings inside. I felt like we had a little bit of an advantage inside and we went to that. In the second half, they hit some shots and we lost our composure a little bit.”

After Dover took a 39-24 lead early in the third quarter, things started to fall apart quickly for the Green Wave. Alvirne picked it up on defense, flustering Dover down low and allowing for few open looks. It didn’t help Dover that the Broncos couldn’t miss, as Purcell’s 3-pointers both came from long range.

“We were making the same mistakes over and over,” Casey said. “We need to recognize that a little bit better and not let one mistake turn into two, turn into three.”

Veronica Moceri scored 22 points for Alvirne to lead all scorers, and she scored in the final seconds of the third period following a steal right under the Dover basket, giving the visitors their 48-44 lead after three stops. Moceri scored three key buckets in the early going of the fourth quarter as Alvirne maintained its lead.